In regards to applying power somewhere other than the down stroke, I think you can accomplish much more over the top of the stroke than you can by doing in real sort of pulling up.
Think about lifting weights in a gym:
Areas in which you can be strong (er):
1. Leg extensions (seated and extending leg at the knee)
2. Leg presses (seated and extending the thighs)
3. Squats (similiar to leg presses)
Weaker exercises
1. Leg curls, you can develop this, but not normally as strong as leg extensions
2. Never done this, but how much weight can you actually lift just by picking your leg up? Not nearly what you can push!
Apply the above to a pedal stroke...
Over the top of the stroke: You can apply a movement very simliar to a leg extension roughly in the 10:30 - 2:00 region of the stroke. To do this you have to use your upper body to brace and create a good platform.
Down stroke: If you begin dropping your heel as you approach the 2:00 area, you can generate tremendous force until around 5:00. At this point the force starts becoming misdirected (although you can still generate it). In a sense, you're trying to stretch the crank.
IF, you let your toe start pointing slightly down at around 4:30, you can get better use of this force from ~4:30 - 5:30 (possibly a little later depending on bike position).
Our body can't really produce "circular" force, so what we're left with is angular (linear) force. We do have a choice however, of how to supply that linear force, and to some extent, what direction to project it.
Because a pedal stroke is circular, all we can really do is break down the circle and attempt to apply linear force tanget to the circle, where it is realistic to do so. Our legs can extend/push with more strength than they can retract/curl, so it only makes to use the strength where it's most beneficial.
On the other hand, our legs don't really act as pistons either. Pistons, move up and down, that's it. Force can be generated in one linear direction, down. Our legs are capable of more than just ...down.
As far as smoothness vs. stomping, I certainly agree. Elite cyclists APPEAR to be pedaling very smoothly. I'm sure the force being applied to the pedals varies greatly over the stroke, but the transitions from no force/less force to a lot of force is very smooth.
Since this thread started I've been paying more attention to my pedaling style, as well as changing things to see the effect. The place where I can tell the most difference is on a long hill.
If I just "stomp" I feel all the mini accelarations as I'm "stomping". This doesn't feel very efficient at all, and proves not to be as my speed eventually drops and legs become more fatigued.
If I apply power over the top of the stroke through 5:30-6:00 I can maintain the same speed with less perceived effort, and do not fatigue nearly as fast. Aside from that, the mini accelerations are gone, speed feels (and is) very constant.
I guess what works for everyone can be different, but in my case I do no significant "pulling" of the pedals. The only exception would be a standing start where I know I pull a lot until I get moving.